1) If you want to just visually show the data then you could either load the data into a database (postgis, oracle etc) and put a geographic server (geoserver, mapserver, arcgis server) in front of that and deliver the data as a WMS to you choice of client (openlayers or leaflet). However this would mean running those applications in a production. The other way to do it is to pre generate the tiles using something like geowebcache and in openlayers or leaflet just read from a local Z/X/Y.png tile pyramid.

2) If you need the actual features (geometry) in the map application then you could either deliver the features to the client using WFS (you would still need database + server) or use UTF Grids which can be created in TileMill or a custom renderer.